Notice that the expected size (over the choice of the hash function \(h\) )
of the intersection of the pre-image of \(z\)  with the set \(A_x\)  is
\(E[|h^{-1}(z) \cap A_x|] = \frac{|A_x|}{|S|} \le 2.1 t \) .
The claim follows by using the following form of the
Chernoff bound [1]}:
\(Pr[X \ge (1 + \delta ) \mu ] \le e^{- \frac{\delta ^2 \mu }{2 + \delta }}\) 
